Draw a vertical line through a normal distribution for each of the following z- score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body. (a). z = 2.20 (b) z = 1.60
(c) z = -1.50 (d) z = - 0.70
I don't know what you mean by "the body."
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to these Z scores.
To draw a vertical line through a normal distribution, you need to understand the concept of z-scores and how they relate to the standard normal distribution. A z-score measures the number of standard deviations a data point is from the mean.
The standard normal distribution has a mean of 0 and a standard deviation of 1. In the standard normal distribution, the body of the distribution is located between -1 and 1.
(a) z = 2.20:
To draw a vertical line at z = 2.20, you will locate the point 2.20 on the x-axis of the standard normal distribution. Since this value is to the right of 0 on the x-axis, the body of the distribution will be on the left side of the line.
To find the proportion in the body, you can use a standard normal distribution table or a statistical software. From the table, you can find the corresponding proportion. For z = 2.20, the proportion in the body would be approximately 0.9857 (rounded to four decimal places). This means that approximately 98.57% of the data falls to the left of the line.
(b) z = 1.60:
To draw a vertical line at z = 1.60, locate the point 1.60 on the x-axis. Since this value is also to the right of 0, the body of the distribution will be on the left side of the line.
Using the standard normal distribution table or statistical software, you can find the proportion in the body. For z = 1.60, the proportion is approximately 0.9452 (rounded to four decimal places). Hence, approximately 94.52% of the data falls to the left of the line.
(c) z = -1.50:
To draw a vertical line at z = -1.50, locate -1.50 on the x-axis. This value is to the left of 0, so the body of the distribution will be on the right side of the line.
Using the standard normal distribution table or statistical software, you can find the proportion in the body. For z = -1.50, the proportion is approximately 0.0668 (rounded to four decimal places). Approximately 6.68% of the data falls to the right of the line.
(d) z = -0.70:
To draw a vertical line at z = -0.70, locate -0.70 on the x-axis. This value is also to the left of 0, so the body of the distribution will be on the right side of the line.
Using the standard normal distribution table or statistical software, you can find the proportion in the body. For z = -0.70, the proportion is approximately 0.2420 (rounded to four decimal places). Approximately 24.20% of the data falls to the right of the line.